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u Formulae For 1 MOVING CHARGES & MAGNETISM 1 11 By Mir Mohammed Abbas II PCMB 'A' CHAPTER FORMULAS & NOTES Important Terms, Definitions & Formulae Top Formulae 1. Lorentz Force :Force on a charge q moving with velocity v in the presence of magnetic and electric fields B and E. F q(vxB E) The magnetic force FB q(vxB) is normal to v and work done by it is zero. 2. Force F on a straight conductor of length and carrying a steady current I placed in a uniform external magnetic field B, F IxB 3. A charge q executes a circular orbit in a plane normal with frequency called the cyclotron frequency given by: c qB 2 m This cyclotron frequency is independent of the particle’s speed and radius. 4. Biot – Savart law asserts that the magnetic field dB due to an element d carrying a steady current I at a point P at a distance r from the current element is: μ d r 0 dB I 3 4π r 5. Magnetic field due to circular coil of radius R carrying a current I at an axial distance x from the centre is B μ0IR2 2 x2 R2 3 /2 At the centre of the coil, 1 CHAPTER FORMULAS & NOTES B 6. 2 μ0I 2R Ampere’s Circuital Law: For an open surface S bounded by a loop C, then the Ampere’s law states that B.d μ0I where I refers o the c current passing through S. If B is directed along the tangent to every point on the perimeter them BL μ0Ie where Ie is the net current enclosed by the closed circuit. 7. Magnetic field at a distance R from a long, straight wire carrying a current I is given by: B μ0I 2R The field lines are circles concentric with the wire. 8. Magnetic field B inside a long Solenoid carrying a current I is B = µ0 nI where n is the number of turns per unit length. For a toriod, B μ0NI 2πr where N is the total numbers of turns and r is the average radius. 9. Magnetic moment m of a planar loop carrying a current I, having N closely wound turns, and an area A, is m NIA Direction of m is given by the right – hand thumb rule: curl and palm of your right hand along the loop with the fingers pointing in the direction of the current. The thumb sticking out gives the direction of m (and A ). When this loop is placed in a uniform magnetic field B, the force F on it is: F = 0 And the torque on it is, mxB CHAPTER FORMULAS & NOTES In a moving coil galvanometer, this torque is balanced by a counter torque due to a spring, yielding. kΦ = NI AB where Φ is the equilibrium deflection and k the torsion constant of the spring. 10. An electron moving around the central nucleus has a magnetic moment μ , given by μ e 2m where is the magnitude of the angular momentum of the circulating electron about the central nucleus. The smallest value of μ is called the Bohr magneton µB and it is µB = 9.27 x 10–24 J/T 3